Question 7: Motion in 1D

Question

A paratrooper jumps from an aeroplane and opens a parachute after 2 s of free fall and starts deaccelerating with $3 \mathrm{~m} / \mathrm{s}^2$. At 10 m height from ground, while descending with the help of parachute, the speed of paratrooper is $5 \mathrm{~m} / \mathrm{s}$. The initial height of the airplane is $\_\_\_\_$ m.
$$ \left(\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2\right) $$

Accepted Answer

Interval 1 :
Free Fall (Before opening the parachute)
The paratrooper is falling under gravity with $\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2$ starting from rest ( $\mathrm{u}_1=0$ ).
$$ 	ext { Time }=\mathrm{t}_1=2 \mathrm{~s} $$
Using equation of motion, the distance covered is
$$ \mathrm{h}_1=\mathrm{u}_1 \mathrm{t}_1+\frac{1}{2} \mathrm{gt}_1^2 $$
$$\Rightarrow $$$$ \mathrm{h}_1=0+\frac{1}{2}(10)(2)^2=20 \mathrm{~m} $$
Let the velocity at the end of interval 1 is $v_1$
$$ \mathrm{v}_1=\mathrm{u}_1+\mathrm{gt}_1=0+(10)(2)=20 \mathrm{~m} / \mathrm{s} $$
Interval 2 :
Deacceleration (After opening the parachute)
The parachute opens, and the paratrooper starts deaccelerating until reaching a height of 10 m above the ground.
Initial velocity for this interval $=\mathrm{u}_2=20 \mathrm{~m} / \mathrm{s}$ (velocity $\mathrm{v}_1$ from interval 1)
Final velocity $=\mathrm{v}_2=5 \mathrm{~m} / \mathrm{s}$
Acceleration $\mathrm{a}=-3 \mathrm{~m} / \mathrm{s}^2$ (deacceleration)
So, the distance covered in interval 2, using the third equation of motion :
$$ \mathrm{v}_2^2=\mathrm{u}_2^2+2 \mathrm{ah}_2 $$
$$\Rightarrow $$ $(5)^2=(20)^2+2(-3) \mathrm{h}_2$
$$\Rightarrow $$ $25=400-6 \mathrm{~h}_2$
$$\Rightarrow $$ $$ \mathrm{h}_2=\frac{375}{6}=62.5 \mathrm{~m} $$
The total initial height,
$$ \mathrm{H}=\mathrm{h}_1+\mathrm{h}_2+\mathrm{h}_{	ext {ground }} $$
$$\Rightarrow $$ $\mathrm{H}=20+62.5+10$
$$\Rightarrow $$ $$ \mathrm{H}=92.5 \mathrm{~m} $$
So, the airplane was at a height of 92.5 m when the paratrooper jumped.
Hence, the correct option is (A).

Answer

92.5

Answer

62.5

Answer

20

Answer

82.5

Motion in 1D

Choose the correct answer: